Issue with integrating a definite integral whose indefinite integral does not exist.

[Leobardo1]

I am still learning how to use the HP Prime Graphing Calculator, but I have a problem. Everytime I try to use int() in CAS mode to integrate 'sin(x^2)' from 0 to 2, but the answer the calculator gives is not the correct answer, it gives a very little number and other calculators my classmates use (TI, Casio, etc) give a whole different answer, what could the problem be? Thanks.

[Tim_Wessman]

Are you doing the calcuation in the CAS screen? (Press the CAS button)

Are you in degrees mode (that would be a very small number)? Tap the  clock area, and tap the angle pi symbol.

[Leobardo1]

The calculator is in radians and I am on CAS mode.

[Tim_Wessman]

Then what is your input, and what are you getting in return?

Also, what is the version of your software? To find it, tap the "Help" button, press TREE. Go to the top and find "About HP Prime" and report the date/version you see there.

[Leobardo1]

My input is: 

int(sin(x^2),x,0,2)

and in return I am getting:

∫(from 0 to 2)sin(x^2)dx

In the past it gave me a number (a wrong number), but I resetted the calculator and now this is what I am getting. Any idea why this happens? TI and Casio calculators give the answer in return, mine just rewrites it.

[Tim_Wessman]

That indicates that there isn't an definitie integral for this equation. In order to integrate this symbolically, you need to have an implementation of the Frensel integral.  Prime does not have that symbolic function (nor does any other graphing/scientific calculator).

What you need to do in this case is perform an APPROXIMATE numerical integration to get the result down to a number. Just press shift-ENTER (see the squiggly = sign, that is the mathematical "approximation" operator). Your number should pop out.

In the past, you may have done this in the HOME screen. When integrating in the home screen, it will automatically evaluate everything down to a "number" result. The  CAS won't automatically do that and keep everything symbolic until you tell it to do something different.

[Maké]

In Approximate mode, is same, with Fresnel result ...

Fresnel integral ... https://en.m.wikipedia.org/wiki/Fresnel_integral

 

See, in comparison with ... Wolfram Alpha ... http://www.wolframalpha.com/input/?i=fresnel+(int(sin(x%5E2),x,0,2))

[Tim_Wessman]

Please stop telling people  to put the CAS into approximate. It is  not recommended, and is not the correct way to do things. It simply will cause MORE problems if you direct people to do this thing.